Constant-volume process

Fig. 8.30 Thermal efficiency of an idealized Otto-cycle process (constant volume process).

If the process is carried out at constant volume, the heat evolved Qi will be equal to an energy change AE2 or, per mole of adsorbate, qi = Ae2 (small capital letters will be used to denote mean molar quantities). Alternatively, the process may be... 

Thus for isobaric processes a new fimction, the enthalpy H, has been introduced and its change A// is more directly related to the heat that must have been absorbed than is the energy change At/. The same reservations about the meanmg of heat absorbed apply in this process as in the constant-volume process. 

C) CONSTANT-TEMPERATURE CONSTANT-VOLUME (ISOTHERMAL-ISOCHORIC) PROCESSES... 

In analogy to the constant-pressure process, constant temperature is defined as meaning that the temperature T of the surroundings remains constant and equal to that of the system in its initial and final (equilibrium) states. First to be considered are constant-temperature constant-volume processes (again Aw = 0). For a reversible process... 

Constant-volume batch diafiltration is the most efficient process mode. Eor species that freely permeate the membrane. 

A turbine-driven screw compressor might be applied to a catalyst regeneration process. The nature of the process then will require constant volume control to maintain a required output temperature in the regenerator. The arrangement is shown in Figure 8-40(b) and would occur as follows ... 

Such hot spots react instantaneously as localized, constant volume sub-explosions (Urtiew and Oppenheim 1966 Lee and Moen 1980). If the mixture around such a sub-explosion is preconditioned sufficiently to ignite on shock compression, a detonation wave will engulf the entire process of flame propagation. 

If the definition of work is limited to mechanical work, an interesting simplification is possible. In this case, AE is merely the heat exchanged at constant volume. This is so because if the volume is constant, no mechanical work can be done on or by the system. Then AE = q. Thus AE is a very useful quantity in constant volume processes. However, chemical and especially biochemical processes and reactions are much more likely to be carried out at constant pressure. In constant pressure processes, AE is not necessarily equal to the heat transferred. For this reason, chemists and biochemists have defined a function that is especially suitable for constant pressure processes. It is called the enthalpy, H, and it is defined as... 

A constant-volume process is called isochoric and, for such processes, the entropy increase is written as... 

The Isochoric Process Figure 2.4 shows the relationship between pcxt and V for an isochoric (constant volume) process going from state a to state b. In this process d V = 0 and tv = 0/... 

A system undergoes a two-step process. In step 1, it absorbs 50. J of heat at constant volume. In step 2, it releases 5 J of heat at 1.00 atm as it is returned to its original internal energy. Find the change in the volume of the system during the second step and identify it as an expansion or compression. 

This equation is sometimes called the van t Hoff isochore, to distinguish it from van t Hoff s osmotic pressure equation (Section 8.17). An isochore is the plot of an equation for a constant-volume process. 

Here Q(t) denotes the heat input per unit volume accumulated up to time t, Cp is the specific heat per unit mass at constant pressure, Cv the specific heat per unit mass at constant volume, c is the sound velocity, oCp the coefficient of isobaric thermal expansion, and pg the equilibrium density. (4) The heat input Q(t) is the laser energy released by the absorbing molecule per unit volume. If the excitation is in the visible spectral range, the evolution of Q(t) follows the rhythm of the different chemically driven relaxation processes through which energy is... 

The calculation takes more than one step, so we need to identify a process. Use Equation to find < calorimeter The heat gained by the calorimeter is supplied by the chemical reaction, so < calorimeter " calonmeter Because the calorimeter operates at constant volume, W = 0, so A " = ( reaction This energy change is for 0.1250 g of octane. Use n — mf M M to determine n, then use Equation to convert to the molar energy change A. S niolar = / n. A... 

In most processes, a reversible absorption of heat is accompanied by a change in temperature, and a calculation of the corresponding entropy change requires an evaluation of the integral of q/T. The term q is related to the heat capacity of the system which is usually expressed as a function of temperature. In a constant volume process, for example, the entropy change is... 

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